water heater venting water outside from what I think is mixer valve

I have a gas powered water heater tank that is continually leaking hot water outside via what I think is an overfill pipe. Having looked at diagrams online, I think it is coming from what is called the mixer valve (please see photos below). I originally thought it was coming from the pressure relief valve (PRV), but that is a separate plastic pipe and is not leaking. Note that I have two vent pipes to outside, one from the PRV and a second from this "mixer valve" thing.

I did test the pressure relief valve and it seems to be working fine. Flows when I open it and stops when closed. When I do operate the PRV, the venting of water from the "mixer valve" stops for a minute then starts dripping again. It is a vigorous drip, maybe a few gallons per day. We have no complaints about the volume or temperature of our hot water.

The water heater is 13 years old and despite having the manual, I do not know what manufacturer it is. There is no ID on the manual, not even a name. We live in a soft water area and this heater is the original install on 1999 house. Note that there is a continual ssshhhh sound like a faucet is running and it is coming from this valve.

I was hoping it was an issue with the PRV and maybe it is - I know little about water heaters.

The valve on the side tank is a T&P valve - the fact you can open it is no perfect indication that it's good.

A mixing valve would require both the hot and cold to connect to it (it's called a tempering valve). I'm not sure, but I think it's a pressure relief valve (again, not a PRV). It could be defective, or could be doing its thing...it would normally be set lower than when the T&P opens. If you have an expansion tank, it could be shot. The city could have raised the supply pressure (new pump, or new water tower, for example).

Thank you Jim. Those are all good, well thought out points. I can see you are an engineer, so that makes sense. I think you are right, it is a pressure relief valve. I am in two minds about just replacing it because as you hinted, there could be other problems and it's just a symptom.

It looks to be an extra valve there.
Some areas required a relief line on the main piping, and none on the water heater. A dumb idea maybe, but that's what some inspectors wanted. Some were done because there was no way to drain a relief off the heater. We could position the relief high enough to get a good gravity drainage off the relief. Since the T&P is being drained outside, it would seem that the one higher up could be deleted.